Modularity, poly­typism, topology, and complexity of crystal structures of inorganic compounds (Review)

The modular approach is a powerful tool in current inorganic crystal chemistry. It enables not only a more detailed analysis of the known structures and the determination of structural relationships between them, but also the prediction of potentially novel structures that can be applied in modern materials science. A large number of examples of compounds with modular structures allows us to state that structural modularity is a widely spread phenomenon among natural and synthetic compounds. The use of the formalism of OD theory makes it possible to analyze the symmetry of polytypes with different crystal structures. In this review, we collected new data published in the last 15 years about OD structures and phenomena of polytypism and modularity in inorganic compounds, as well as the topological approach to the analysis of crystal structures.